Intelligent Vehicle Lane-Change Trajectory Planning on Slippery Road Surface Using Nonlinear Programming

<div>Single lane changing is one of the typical scenarios in vehicle driving. Planning an appropriate lane change trajectory is crucial in autonomous and semi-autonomous vehicle research. Existing polynomial trajectory planning mostly uses cubic or quintic polynomials, neglecting the lateral jerk constraints during lane changes. This study uses seventh-degree polynomials for lane change trajectory planning by considering the vehicle lateral jerk constraints. Simulation results show that the utilization of the seventh-degree method results in a 41% reduction in jerk compared to the fifth-degree polynomial. Furthermore, this study also proposes lane change trajectory schemes that can cater to different driving styles (e.g., safety, efficiency, comfort, and balanced performance). Depending on the driving style, the planned lane change trajectory ensures that the vehicle achieves optimal performance in one or more aspects during the lane change process. For example, with the trajectory that provides the best comprehensive performance under given constraints (initial speed of 20 m/s, lane width of 3.5 m, and a longitudinal distance of 50 m to the obstacle in front), the four-wheel steering model predictive control can effectively track the planned trajectory, with the maximum jerk value being 6.4 m/s<sup>3</sup> and the longitudinal speed after lane change being approximately 12.6 m/s. Although this study assumes specific longitudinal displacement before and after the lane change, the methodology is applicable to other scenarios. For example, it can determine the shortest longitudinal displacement and the optimal lane change trajectory given predefined vehicle speeds and maximum lateral acceleration conditions. The lane change trajectories developed in this study can be directly applied to the system design of autonomous vehicles.</div>

Investigating model and impacts of lane-changing execution process based on CA model

Trajectory planning and tracking of lane change are critical technologies for autonomous buses. Characteristics of the buses susceptible to stability problems resulting from the high height, large passenger capacity and long lengths, coupling the dynamic traffic with the dynamic changes in the states of adjacent vehicles and road adhesion coefficient, put forward great challenges in lane change for autonomous buses (ABs). To cope with the foregoing challenges, a framework is proposed to achieve the trajectory planning and tracking of dynamic lane change for ABs. For trajectory planning approach, the trajectory planning and replanning is optimized in the safe range of longitudinal length of the lane-changing trajectory to obtain the real-time reference trajectory, combining consideration of vehicle yaw, roll stability and lane-changing efficiency. The minimum longitudinal length of lane-changing trajectory determined by the yaw stability and roll stability of ABs, combined with the maximum length formed by the adjacent vehicles with dynamic states, form the real-time safe range for lane-changing trajectory planning. For trajectory tracking approach, a tracking approach using model predictive control based on multipoint preview is proposed to achieve the real-time planned trajectory tracking considering buses stability. The effectiveness of the proposed strategy is evaluated by simulating an experimentally validated Trucksim model in different dynamic traffic scenarios to demonstrate the capability of the strategy in trajectory planning and tracking, and guaranteeing vehicle stability for dynamic lane change of ABs.

Energy-efficient lane-change motion planning for personalized autonomous driving

At present, the lane changing technology for a single driving environment has been relatively mature, but the actual situations are much more complicated, such as the changing curvature and the changes in road conditions. In this paper, a new lane changing obstacle avoidance control strategy for the variable curvature road was proposed. It has two stages including path planning for variable curvature lane changing and inverse system decoupling (ISD) control for path tracking. The first stage established the lane changing path models for the variable curvature road. A longitudinal-lateral safe distance model was proposed to constrain the safe boundary of the lane changing path. The second stage proposed a dynamic decoupling method for longitudinal and lateral motion based on the inverse system decoupling, a direct yaw moment and active front wheel steering coordinated control method was designed. The inverse system decoupling algorithm can correct the single point preview (SPP) method to improve the stability and the path tracking accuracy in the lane changing obstacle avoidance process. The strategy was simulated by CarSim/Simulink co-simulation, and the experiments were carried out on the hardware-in-the-loop platform. The results show that the proposed control strategy can effectively avoid obstacles when the vehicle is driving on the variable curvature road. Besides, for the different road conditions and the strong non-linearity generated during the lane changing process, the control strategy can reduce the tracking error by a maximum of 32.7%, both the yaw rate and side slip angle can be controlled in a smaller range.

Lane change (LC) is a maneuver that allows drivers to enter into a lane that suits their requirements and comfort. The LC process requires the driver to assess its neighborhood traffic in its original and target lanes before undertaking the maneuver. Other vehicles in the neighborhood also need to adjust for safe lane change. The LC trajectory is determined by the accuracy of these subjective assessments as well as the state of traffic. An erroneous assessment by LC vehicle or neighboring vehicles or an incorrect maneuver can cause collision. The collision can be prevented if the LC trajectory can be predicted and the feasibility of LC can be communicated to different vehicles involved in this process. . In the present paper, neural network is used for long term forecast of the lane change trajectory and for short term near future positions of the LC vehicle. The neural network is trained using past LC trajectories of different vehicles. The trained network is then used for long and short term forecast of the vehicle’s positions during LC. Simulation results with actual filed data observed data indicates that neural network is able to learn LC maneuvers and is able to perform short term prediction with sufficient accuracy.

<div class="section abstract"><div class="htmlview paragraph">The automatic lane change assist system is an intelligent driving assistance technology oriented to traffic safety, which requires trajectory planning of the lane change maneuver based on the lane change decision. A typical scene of lane change for overtaking is selected, where the front vehicle in the same lane and the rear vehicle in the left lane are deemed to be potential dangerous vehicles through the lane change. Lane change trajectory equation is first established according to the general law of steering wheel angle through lane changes. Based on the relative position, velocity and acceleration information of the dangerous vehicles and the lane change vehicle, motions of these surrounding dangerous vehicles are predicted. At the same time, a multi-objective optimization function is established based on the relative longitudinal safety boundary. The objectives are the minimum safety distance, the lane change time and the front wheel angle. The trajectory planning algorithm of the lane change assist based on the model predictive control with multi-objective is then studied. The influence of vehicle speed on trajectory tracking is analyzed in this paper, then the feasibility and robustness of the algorithm is verified. In addition, the complexity of the model is simplified in considering of real-time demand while accuracy is still guaranteed. Simulation and experimental results show that the trajectory planning algorithm based on the model predictive control with multi - objective has greater improvements of those objectives of lane change compared with PID control. The proposed trajectory optimization algorithm can provide reference for the automatic lane change assist system.</div></div>

A dynamic lane-changing decision and trajectory planning model of autonomous vehicles under mixed autonomous vehicle and human-driven vehicle environment

Nowadays, with more and more attention being paid to the characteristics and experience of drivers, a large number of driver classification algorithms have emerged. However, these methods basically cannot be adjusted independently to each driver. Therefore, this paper proposes a self-learning lane change motion planning system considering the driver’s personality. Firstly, the method of driver data acquisition and processing is determined to obtain and extract the lane change data. Then, the planning system built in this paper is explained from two aspects: lane change trigger and lane change trajectory. According to the artificial potential field theory, an obstacle driving risk field is established to evaluate the acceptance of environmental risks of different drivers, and to achieve personalized lane change triggers through online statistics. At the same time, the safety of lane change is ensured by establishing the safety distance model of the target lane. On the other hand, the driver characteristic coefficient Jc and the driver reaction and operation time td are introduced into the traditional Gaussian-distributed model to establish a personalized lane change trajectory planning model, in which the parameters are obtained from offline and online learning. Offline learning is based on DTW for trajectory matching, and uses AP clustering to obtain the generalized parameters; Online learning uses LSTM to achieve personalized updates. Finally, this paper selected 15 drivers for verification, and the results show that the motion planning system can well reproduce the lane change behavior of the driver.

Vehicle lane changing is one of the most important topics in autonomous driving and is the behavior most likely to cause vehicle accidents. In order to optimize the performance of vehicle lane change by controlling the speed of the vehicle, which makes the lane change safer, more efficient, and more eco-friendly, a causal inference-based speed control framework is proposed in this study. First, variables affecting the lane change efficiency are selected and their treatment effects are obtained by conducting causal effect analysis and causal refutation analysis. Second, the conditional average treatment effect is estimated by taking the safety and eco-friendly requirements into consideration and applying the double machine learning version causal forest model. Finally, a controller is built, and grid search is used to optimize lane change decision-making. By conducting numerical experiments, the average lane change duration decreased by 5.9% and average velocity increased from 7.165 m/s to 7.791 m/s. The results show that the framework has good performance on improving the efficiency and environmental friendliness of a lane change process while ensuring safety. The proposed framework provides a new approach to speed control for discretionary lane-changing behavior. The approach can be well adapted to a vehicle-to-vehicle communication environment and is expected to be applied to vehicle-assisted driving systems in the future.

In order to accurately predict the lane‐changing trajectory of the vehicle and improve the driving safety of the vehicle, a lane‐changing trajectory prediction model based on the combination of convolutional neural network (CNN) and bidirectional long short‐term memory (BiLSTM) neural network is proposed by comprehensively considering the historical driving behavior, the spatial characteristics of surrounding vehicles and the bidirectional time sequence information of the vehicle trajectory. Firstly, the vehicle trajectory data are filtered and smoothed, and it is divided into three categories: left lane change, right lane change, and straight driving, and a lane change trajectory sample set is constructed. Secondly, CNN‐BiLSTM model is constructed to identify the sample set of lane‐changing trajectory. Considering the interaction between vehicles in the driving process, the information of predicted vehicle, and surrounding vehicles is taken as the input of the model. The extracted feature vector is input to the BiLSTM layer for prediction after the CNN layer feature extraction, and the horizontal and vertical coordinates of the target vehicle at the next time are output. Thirdly, the trajectory data of the US‐101 dataset in NGSIM is selected to verify the performance of the CNN‐BiLSTM model, and at the same time, it is compared with models such as CNN‐LSTM, long short‐term memory (LSTM), BiLSTM, and CNN‐GRU‐Att. Finally, the verification result shows that the overall fitting degree of the vehicle lane change trajectory prediction of the proposed model reaches 99.50%, and the mean square error and mean absolute error are 0.0003076 and 0.01417, which are improved compared with other models. In the meanwhile, the research on multistep trajectory prediction in different prediction time domains is carried out. It was found that the longer the prediction time domain is, the lower the prediction performance of the model decreases, but the prediction accuracy still reached more than 96%, and it was able to accurately predict the lane change trajectory.

The paper considers the application of neural networks to model driver decisions to change lane on a dual carriageway road. The lane changing process is treated as consisting of two decisions, namely motivation and opportunity. Separate backpropagation neural networks are applied to represent each of the two decisions. The trained motivation and opportunity neural network models are linked to produce a layered network which represents the complete lane changing process. Separate models are developed to represent the nearside to offside lane changing decision, and the offside to nearside lane changing decision. This paper describes the development of the model of the nearside to offside lane changing decision.For model development, data were collected from several subject vehicle drivers. The results are presented and the implications considered. Selected data were applied to train the neural networks and then an independent subset of data were used to assess performance. When the complete nearside lane changing neural network model was presented with the unseen test examples, 93.3% of the examples were correctly predicted as a lane change or no lane change. These results are shown to be a considerable improvement on those obtained previously.

Enhancing lane changing trajectory prediction on highways: A heuristic attention-based encoder-decoder model

<div class="section abstract"><div class="htmlview paragraph">After obtaining the optimal trajectory through the lane change decision and trajectory planning, the last key technology for the automatic lane change assist system is to carry out the precise and rapid steering actuation according to the front wheel angle demand. Therefore, an automatic lane change system model including a BLDCM (brushless DC motor) model, a steering system model and a vehicle dynamics model is first established in this paper. Electromagnetic characteristics of the motor, the moment of the inertia and viscous friction etc. are considered in these models. Then, a SMC (Sliding Mode Control) algorithm for the steering system is designed to follow the steering angle input. The control torque of the steering motor is obtained through the system model according to steering angle demand. After that, the control current is calculated considering of electromagnetic characteristics of the BLDCM. Debugging and optimization of the control algorithm are done through simulations. Also, different steering input and uncertain disturbance torque are successively loaded on the simulation model to test the tracking performance and robustness of the control algorithm. Simulation results are compared with the PID’s and show that under different steering inputs, the steering system with the proposed controller manifests a better tracking performance. Even if large parameter uncertainties are taken into consideration, tracking error will not be enlarged obviously, which indicates that the SMC has good robustness. These results can provide reference for precise steering angle control of the automatic lane change assist system by considering of different parts of the steering system, steering motor, steering transmission linkage, and steered wheels.</div></div>

Current lane-based microscopic traffic simulators combine car-following and lane changing logic to describe the (often discrete) lateral vehicle motion on multi-lane road segments. However, the simulated lateral trajectories are physically unplausible and inside-lane behavior such as lane-keeping and curve negotiation cannot be modelled. In this work, we integrate lateral vehicle dynamics and yaw motion into a traffic simulation framework, aiming to describe lateral motion and vehicle interactions with more precision. The resulting framework consists of two coupled layers, an upper tactical level that plans maneuvers such as lane-changing; and a lower operational layer with a control module (steering and acceleration control) that operates in a closed loop with the bicycle model of vehicle dynamics. The feedback mechanism between the layers allows for dynamic trajectory re-planning. Unlike the microscopic traffic models, the proposed framework accounts for lateral vehicle dynamics and yaw motion; provides additional variables such as vehicle heading and front wheel steering angle; and is hence termed as submicroscopic. Case study results demonstrate the power of the framework to include lateral maneuvers such as curve negotiation, corrective steering, lane change abortion and fragmented lane changing. The framework was operationalized to model multi-lane traffic flow consisting of human-driven vehicles. At the macroscopic level, the traffic flow simulation can reproduce phenomena such as capacity drop. Thus the framework preserves the properties of the component models and at the same time describe the continuous 2-D planar movement of vehicles.